0 0.5 1 1.5 2 2.5

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32

34

36

38

40

42

44

46

rate (bpp)

PS

NR

(d

B)

No noise processing, conventional synthesisNo noise processing, dual frame synthesisWith noise processing A, conventional synthesis

0 0.5 1 1.5 2 2.530

32

34

36

38

40

42

44

46

rate (bpp)

PS

NR

(d

B)

No noise processing, conventional synthesisNo noise processing, dual frame synthesisWith noise processing A, conventional synthesisWith noise processing B, conventional synthesis

0 0.5 1 1.5 2 2.530

32

34

36

38

40

42

44

rate (bpp)

PS

NR

(d

B)

No noise processing, conventional synthesisNo noise processing, dual frame synthesisWith noise processing A, conventional synthesis

0 0.5 1 1.5 2 2.530

32

34

36

38

40

42

44

rate (bpp)

PS

NR

(d

B)

No noise processing, conventional synthesisNo noise processing, dual frame synthesisWith noise processing A, conventional synthesisWith noise processing B, conventional synthesis

Noise Processing for Simple Laplacian Pyramid Synthesis Based on Dual Frame Reconstruction

Aditya Mavlankar, David Chen, Sameh Zakhary, Markus Flierl and Bernd GirodInformation Systems Laboratory, Stanford University, Stanford, CA 94305, USA

{maditya, dmchen, zakhary, mflierl, bgirod} @ stanford.edu

Laplacian Pyramid: Background

• Proposed by Burt and Adelson in 1983• Laplacian pyramid (LP) is overcomplete• Key differences of LP from critically sampled

filterbanks– Freedom in the design of filters– Multiple reconstruction methods– Reduced aliasing in highpass subbands

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Single level decompositio

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Single level reconstructio

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Quantization

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Dual Frame Reconstruction

• Proposed by Do and Vetterli in 2003•

Analysis operator has multiple left-inverses• Optimal synthesis operator

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Conventional Reconstructio

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Dual Frame Reconstructio

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• Proposed structure implements if and only if– , i.e., biorthogonality– , i.e., is an orthogonal

projector• Practically, the proposed structure offers gains

even if above conditions are not strictly met, e.g., about 1 dB gain for the 9/7 filters.

•

Encoder-Side Noise Processing

• Keep simple conventional reconstruction• Achieve gains offered by dual frame

reconstruction• Since we process at the encoder itself.

or equivalently,

Extension to Multiple Levels

(a) Conventional encoder

(b) Noise processing method A

(c) Noise processing method B

Experimental Results

Lena (512x512)

Einstein (512x512)Conclusions

• Reconstruction procedure proposed by Do and Vetterli achieves roughly 1 dB gain for 9/7 filters

• Similar gain is achievable by our proposed encoder-side noise processing while retaining simple synthesis

• The same simple decoder can be employed for both open-loop and closed-loop encoding; simple decoder is optimal for closed-loop encoding anyway

• Overall complexity of encoder and decoder combined is the same as for dual frame reconstruction; roughly half of the complexity is shifted from the decoder to the encoder

One decomposition level (left) and four decomposition levels (right)

Contact

Conventional Reconstruction